A Sequential Linear Programming Coordination Algorithm for Analytical Target Cascading

2007 ◽  
Author(s):  
Jeongwoo Han ◽  
Panos Papalambros
Keyword(s):  
Linear Programming ◽  
Optimization Problems ◽  
Trust Region ◽  
Test Problems ◽  
Sequential Linear Programming ◽  
Analytical Target Cascading ◽  
Step Size ◽  
Normal Distributions ◽  
Coordination Strategy ◽  
Target Cascading

Decomposition-based strategies, such as analytical target cascading (ATC), are often employed in design optimization of complex systems. Achieving convergence and computational efficiency in the coordination strategy that solves the partitioned problem is a key challenge. A new convergent strategy is proposed for ATC, which coordinates the interactions among subproblems using sequential lineralizations. Linearity of subproblems is maintained using L∞ norms to measure deviations between targets and responses. A subproblem suspension strategy is used to temporarily suspend inclusion of subproblems that do not need significant redesign, based on trust region and target value step size. The proposed strategy is intended for use in optimization problems where sequential linearizations are typically effective, such as problems with extensive monotonicities, large number of constraints relative to variables, and propagation of probabilities with normal distributions. Experiments with test problems show that, relative to standard ATC coordination, the number of subproblem evaluations is reduced considerably while maintaining accuracy.

A Sequential Linear Programming Coordination Algorithm for Analytical Target Cascading

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Jeongwoo Han ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Test Problems ◽  
Analytical Target Cascading ◽  
Step Size ◽  
Coordination Strategy ◽  
Target Cascading ◽  
Solution Accuracy

Decomposition-based strategies, such as analytical target cascading (ATC), are often employed in design optimization of complex systems. Achieving convergence and computational efficiency in the coordination strategy that solves the partitioned problem is a key challenge. A new convergent strategy is proposed for ATC that coordinates interactions among subproblems using sequential linearizations. The linearity of subproblems is maintained using infinity norms to measure deviations between targets and responses. A subproblem suspension strategy is used to suspend temporarily inclusion of subproblems that do not need significant redesign, based on trust region and target value step size. An individual subproblem trust region method is introduced for faster convergence. The proposed strategy is intended for use in design optimization problems where sequential linearizations are typically effective, such as problems with extensive monotonicities, a large number of constraints relative to variables, and propagation of probabilities with normal distributions. Experiments with test problems show that, relative to standard ATC coordination, the number of subproblem evaluations is reduced considerably while the solution accuracy depends on the degree of monotonicity and nonlinearity.

A Note on the Convergence of Analytical Target Cascading With Infinite Norms

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Jeongwoo Han ◽  
Panos Y. Papalambros
Keyword(s):  
Linear Programming ◽  
Multidisciplinary Design Optimization ◽  
Optimization Method ◽  
Multidisciplinary Design ◽  
Strong Monotonicity ◽  
Sequential Linear Programming ◽  
Analytical Target Cascading ◽  
Hierarchical Systems ◽  
Coordination Strategy ◽  
Target Cascading

Analytical target cascading (ATC) is a multidisciplinary design optimization method for multilevel hierarchical systems. To improve computational efficiency, especially for problems under uncertainty or with strong monotonicity, a sequential linear programming (SLP) algorithm was previously employed as an alternate coordination strategy to solve ATC and probabilistic ATC problems. The SLP implementation utilizes L∞ norms to maintain the linearity of SLP subsequences. This note offers a proof that there exists a set of weights such that the ATC algorithm converges when L∞ norms are used. Examples are also provided to illustrate the effectiveness of using L∞ norms as a penalty function to maintain the formulation linear and differentiable. The examples show that the proposed method provides more robust results for linearized ATC problems due to the robustness of the linear programming solver.

Diagonal Quadratic Approximation for Parallelization of Analytical Target Cascading

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Yanjing Li ◽  
Zhaosong Lu ◽  
Jeremy J. Michalek
Keyword(s):  
Optimization Problems ◽  
Computational Cost ◽  
Descent Method ◽  
Quadratic Approximation ◽  
Test Problems ◽  
Analytical Target Cascading ◽  
Decomposition Approach ◽  
Diagonal Quadratic Approximation ◽  
Target Cascading ◽  
Nested Loop

Analytical target cascading (ATC) is an effective decomposition approach used for engineering design optimization problems that have hierarchical structures. With ATC, the overall system is split into subsystems, which are solved separately and coordinated via target/response consistency constraints. As parallel computing becomes more common, it is desirable to have separable subproblems in ATC so that each subproblem can be solved concurrently to increase computational throughput. In this paper, we first examine existing ATC methods, providing an alternative to existing nested coordination schemes by using the block coordinate descent method (BCD). Then we apply diagonal quadratic approximation (DQA) by linearizing the cross term of the augmented Lagrangian function to create separable subproblems. Local and global convergence proofs are described for this method. To further reduce overall computational cost, we introduce the truncated DQA (TDQA) method, which limits the number of inner loop iterations of DQA. These two new methods are empirically compared to existing methods using test problems from the literature. Results show that computational cost of nested loop methods is reduced by using BCD, and generally the computational cost of the truncated methods is superior to the nested loop methods with lower overall computational cost than the best previously reported results.

Diagonal Quadratic Approximation for Parallelization of Analytical Target Cascading

2007 ◽  
Author(s):  
Yanjing Li ◽  
Zhaosong Lu ◽  
Jeremy J. Michalek
Keyword(s):  
Optimization Problems ◽  
Computational Cost ◽  
Descent Method ◽  
Quadratic Approximation ◽  
Test Problems ◽  
Analytical Target Cascading ◽  
Decomposition Approach ◽  
Diagonal Quadratic Approximation ◽  
Target Cascading ◽  
Nested Loop

Analytical Target Cascading (ATC) is an effective decomposition approach used for engineering design optimization problems that have hierarchical structures. With ATC, the overall system is split into subsystems, which are solved separately and coordinated via target/response consistency constraints. As parallel computing becomes more common, it is desirable to have separable subproblems in ATC so that each subproblem can be solved concurrently to increase computational throughput. In this paper, we first examine existing ATC methods, providing an alternative to existing nested coordination schemes by using the block coordinate descent method (BCD). Then we apply diagonal quadratic approximation (DQA) by linearizing the cross term of the augmented Lagrangian function to create separable subproblems. Local and global convergence proofs are described for this method. To further reduce overall computational cost, we introduce the truncated DQA (TDQA) method that limits the number of inner loop iterations of DQA. These two new methods are empirically compared to existing methods using test problems from the literature. Results show that computational cost of nested loop methods is reduced by using BCD and generally the computational cost of the truncated methods, TDQA and ALAD, are superior to other nested loop methods with lower overall computational cost than the best previously reported results.

Improved Trust Region Based MPS Method for High-Dimensional Expensive Black-Box Problems

2013 ◽  
Author(s):  
George H. Cheng ◽  
Adel Younis ◽  
Kambiz Haji Hajikolaei ◽  
G. Gary Wang
Keyword(s):  
Optimization Problems ◽  
Trust Region ◽  
Black Box ◽  
High Dimensional ◽  
Test Problems ◽  
Design Variables ◽  
Low Dimensionality ◽  
Improve Algorithm ◽  
Improved Performance ◽  
Better Than

Mode Pursuing Sampling (MPS) was developed as a global optimization algorithm for optimization problems involving expensive black box functions. MPS has been found to be effective and efficient for problems of low dimensionality, i.e., the number of design variables is less than ten. A previous conference publication integrated the concept of trust regions into the MPS framework to create a new algorithm, TRMPS, which dramatically improved performance and efficiency for high dimensional problems. However, although TRMPS performed better than MPS, it was unproven against other established algorithms such as GA. This paper introduces an improved algorithm, TRMPS2, which incorporates guided sampling and low function value criterion to further improve algorithm performance for high dimensional problems. TRMPS2 is benchmarked against MPS and GA using a suite of test problems. The results show that TRMPS2 performs better than MPS and GA on average for high dimensional, expensive, and black box (HEB) problems.

scholarly journals An Enhanced Analytical Target Cascading and Kriging Model Combined Approach for Multidisciplinary Design Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Ping Jiang ◽  
Jianzhuang Wang ◽  
Qi Zhou ◽  
Xiaolin Zhang
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Kriging Model ◽  
Multidisciplinary Design ◽  
High Approximation ◽  
Engineering Systems ◽  
Analytical Target Cascading ◽  
Combined Approach ◽  
Coordination Strategy ◽  
Target Cascading

Multidisciplinary design optimization (MDO) has been applied widely in the design of complex engineering systems. To ease MDO problems, analytical target cascading (ATC) organizes MDO process into multilevels according to the components of engineering systems, which provides a promising way to deal with MDO problems. ATC adopts a coordination strategy to coordinate the couplings between two adjacent levels in the design optimization process; however, existing coordination strategies in ATC face the obstacles of complicated coordination process and heavy computation cost. In order to conquer this problem, a quadratic exterior penalty function (QEPF) based ATC (QEPF-ATC) approach is proposed, where QEPF is adopted as the coordination strategy. Moreover, approximate models are adopted widely to replace the expensive simulation models in MDO; a QEPF-ATC and Kriging model combined approach is further proposed to deal with MDO problems, owing to the comprehensive performance, high approximation accuracy, and robustness of Kriging model. Finally, the geometric programming and reducer design cases are given to validate the applicability and efficiency of the proposed approach.

scholarly journals A randomized adaptive trust region line search method

2020 ◽  
Vol 10 (2) ◽  
pp. 259-263
Author(s):  
Saman Babaie-Kafaki ◽  
Saeed Rezaee
Keyword(s):  
Simulated Annealing ◽  
Numerical Experiments ◽  
Line Search ◽  
Optimization Problems ◽  
Trust Region ◽  
Search Method ◽  
Test Problems ◽  
Unconstrained Optimization Problems ◽  
Line Search Method ◽  
Region Line

Hybridizing the trust region, line search and simulated annealing methods, we develop a heuristic algorithm for solving unconstrained optimization problems. We make some numerical experiments on a set of CUTEr test problems to investigate efficiency of the suggested algorithm. The results show that the algorithm is practically promising.

A randomized nonmonotone adaptive trust region method based on the simulated annealing strategy for unconstrained optimization

2019 ◽  
Vol 12 (3) ◽  
pp. 389-399
Author(s):  
Saman Babaie-Kafaki ◽  
Saeed Rezaee
Keyword(s):  
Simulated Annealing ◽  
Unconstrained Optimization ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Test Problems ◽  
Content Type ◽  
Unconstrained Optimization Problems ◽  
Randomization Scheme ◽  
Enhance Efficiency

PurposeThe purpose of this paper is to employ stochastic techniques to increase efficiency of the classical algorithms for solving nonlinear optimization problems.Design/methodology/approachThe well-known simulated annealing strategy is employed to search successive neighborhoods of the classical trust region (TR) algorithm.FindingsAn adaptive formula for computing the TR radius is suggested based on an eigenvalue analysis conducted on the memoryless Broyden-Fletcher-Goldfarb-Shanno updating formula. Also, a (heuristic) randomized adaptive TR algorithm is developed for solving unconstrained optimization problems. Results of computational experiments on a set of CUTEr test problems show that the proposed randomization scheme can enhance efficiency of the TR methods.Practical implicationsThe algorithm can be effectively used for solving the optimization problems which appear in engineering, economics, management, industry and other areas.Originality/valueThe proposed randomization scheme improves computational costs of the classical TR algorithm. Especially, the suggested algorithm avoids resolving the TR subproblems for many times.

A Note on Wedge Trust Region Radius Update

2011 ◽  
Vol 52-54 ◽  
pp. 926-931
Author(s):  
Qing Hua Zhou ◽  
Feng Xia Xu ◽  
Yan Geng ◽  
Ya Rui Zhang
Keyword(s):  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Test Problems ◽  
Region Method ◽  
Derivative Free Optimization ◽  
Derivative Free ◽  
Updating Rule

Wedge trust region method based on traditional trust region is designed for derivative free optimization problems. This method adds a constraint to the trust region problem, which is called “wedge method”. The problem is that the updating strategy of wedge trust region radius is somewhat simple. In this paper, we develop and combine a new radius updating rule with this method. For most test problems, the number of function evaluations is reduced significantly. The experiments demonstrate the effectiveness of the improvement through our algorithm.

scholarly journals AN IMPROVED ADAPTIVE TRUST-REGION METHOD FOR UNCONSTRAINED OPTIMIZATION

2014 ◽  
Vol 19 (4) ◽  
pp. 469-490 ◽  
Author(s):  
Hamid Esmaeili ◽  
Morteza Kimiaei
Keyword(s):  
Unconstrained Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Standard Test ◽  
Test Problems ◽  
Unconstrained Optimization Problems ◽  
Large Scale Problems ◽  
Adaptive Radius

In this study, we propose a trust-region-based procedure to solve unconstrained optimization problems that take advantage of the nonmonotone technique to introduce an efficient adaptive radius strategy. In our approach, the adaptive technique leads to decreasing the total number of iterations, while utilizing the structure of nonmonotone formula helps us to handle large-scale problems. The new algorithm preserves the global convergence and has quadratic convergence under suitable conditions. Preliminary numerical experiments on standard test problems indicate the efficiency and robustness of the proposed approach for solving unconstrained optimization problems.

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